Different types of queue length information with a constant delay have been used, see [1]} for example, which considers so-called mean-field queue length information with a constant delay. Other types of information that have been considered include delayed velocity information and moving average information, see [2]}, [3]}, [4]}, [5]}. Some of the literature has examined queueing systems where the delay is not constant. For example, a queueing model that uses delayed updating information is examined in [6]}, [7]}. Additionally, queueing models with distributed delays have been studied by considering distributed delay equation models in [8]}, [9]}, though it is worth noting that distributed delay models exhibit different dynamics in general than simply replacing the constant delay with a random variable in standard models, as discussed in [10]}.
